Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-31T12:46:05.761Z Has data issue: false hasContentIssue false
  • English
  • Français

The inverse Goldbach problem

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  26 February 2010

Christian Elsholtz
Christian Elsholtz
Affiliation:
Institut fur Mathematik, TU Clausthal, Erzstrasse 1, D-38678 Clausthal-Zellerfeld, Germany. E-mail: elsholtz@math.tu-clausthal.de.
Get access

Abstract

Improved upper and lower bounds of the counting functions of the conceivable additive decomposition sets of the set of primes are established. Suppose that where, ℝ′ differs from the set of primes in finitely many elements only and .

It is shown that the counting functions A(x) of ℐ and B(x) of ℬ for sufficiently large x, satisfy

MSC classification

Secondary: 11P32: Goldbach-type theorems; other additive questions involving primes

Information

Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 151 - 158
Copyright
Copyright © University College London 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Elsholtz, C.. A remark on Hofmann and Wolke's additive decompositions of the set of primes. Arch. Math. 76 (2001), 30–33.CrossRefGoogle Scholar
2.Erdős, P.. Problems and results in number theory. Number Theory Day, New York, (1976). Springer Lecture Notes in Math. 626, 43–72.CrossRefGoogle Scholar
3.Gallagher, P. X.. A larger sieve. Acta Arith. 18 (1971), 77–81.CrossRefGoogle Scholar
4.Hornfeck, B.. Ein Satz fiber die Primzahlmenge. Math. Z., 60 (1954), 271–273 (see also the correction in vol. 62 (1955), page 502).CrossRefGoogle Scholar
5.Hofmann, A. and Wolke, D.. On additive decompositions of the set of primes. Arch. Math. 67 (1996), 379–382.CrossRefGoogle Scholar
6.Mann, H.. Addition Theorems: The Addition Theorems of Group Theory and Number Theory. Wiley-Interscience, New York-London-Sydney (1965).Google Scholar
7.Montgomery, H. L.. The analytic principle of the large sieve. Bull. Amer. Math. Soc, 84 (1978), 547–567.CrossRefGoogle Scholar
8.Ostmann, H.-H.. Additive Zahlentheorie, 1. Teii. Allgemeine Untersuchungen, Springer-Verlag, Berlin-Heidelberg-New York (1968).Google Scholar
9.Pomerance, C., Sarkozy, A. and Stewart, C. L.. On divisors of sums of integers, III. Pacific J. Math., 133 (1988), 363–381.CrossRefGoogle Scholar
10.Vaughan, R. C.. Some applications of Montgomery's sieve. J. Number Theory, 5 (1973), 64– 79.CrossRefGoogle Scholar
11.Wirsing, E.. Uber additive Zerlegungen der Primzahlmenge. (Unpublished manuscript, an abstract can be found in Tagungsbericht 28/1972, Oberwolfach.).Google Scholar
12.Wirsing, E.. Problem at the problem session. Abstracts of the Oberwolfach Conference 10/1998.Google Scholar